Tissue Preparation and Image Acquisition

In the present study, all the images were obtained from developing mouse kidneys. The animal experiments were performed in accordance with the code of Ethics of World Medical Association (Declaration of Helsinki) and were approved by the Medical Ethics Committee of China Medical University.

C57/BL/6J mouse kidneys from three embryonic 17^th day fetuses (E17) and from three postnatal 7^th day pups (P7) were studied. The fetal kidneys were removed a few minutes after injection of pentobarbital sodium (50 mg/kg body weight) into the peritoneal cavity of the pregnant mice. The pup kidneys were preserved by perfusion fixation through the heart with a mixture solution of 4% paraformaldehyde and 1% glutaraldehyde in 0.06 M sodium cacodylate buffer, pH 7.4. All the kidneys or tissue blocks were further fixed for 1 h in 1% OsO₄ in 0.1 M sodium cacodylate buffer, and embedded in Epon 812, then cut into serial semi-thin (2.5-μm-thick) sections using a Reichert Ultracut microtome (Reichert, Wienna, Austria). These consecutive sections were stained with toluidine blue for morphological recognition. In all, about 600 sections from each of the three E17 kidneys and about 800 sections from each of the P7 kidneys were obtained. The serial sections were used for the purpose of the 3D reconstruction and functional analysis of the mouse developing kidneys, as previously reported [16].

Stacks of the tissue images were captured using a slide scanner (NanoZoomer Digital Pathology, Hamamatsu, Japan) equipped with a 40× objective lens. The original image size was 10240 × 8196 pixels, whereby each pixel corresponded to 0.46 μm × 0.46 μm.

Sequential Histogram Fitting Algorithm

In the brightness histogram of a microscopic image (Fig 1), the columns on the leftmost part represent the frequencies of the pixels with the lowest gray values, which normally corresponds to the artifacts in the image; while those on the rightmost part represent the frequencies of the pixels with the highest gray values, corresponding to the bright background without tissue in the image; the middle part of the histogram represents the dynamic range, reflecting the frequencies of the gray values of the tissue structures. So, the dynamic range varies in shape from image to image. For example, the renal tubule wall is stained dark, which is reflected on the left part of the dynamic range; while the lumen of the tubules in kidney tissue is either not stained or stained very light, which is reflected on the right part of the dynamic range.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. Schematic diagram of SHFA.

(A) The histogram of the original image; (B) The desired histogram. The desired image is generated by gray value transformation from the original histogram to the desired histogram.

https://doi.org/10.1371/journal.pone.0127855.g001

Most algorithms for adjustment of brightness and contrast are based on histogram operations, e.g. the shifting operation for brightness compensation, and the extension operation for contrast enhancement. However, with respect to a series of images, one single operation, either shifting or extending, may not meet the demands for both brightness and contrast homogenization at the same time. Therefore, the strategy is to take both brightness and contrast adjustment into consideration at the same time.

The principle of our method is that the shape of each histogram is only related to the morphological tissue structures in the image; so under optimal conditions of tissue preparation and image acquisition, the individual histograms should be consecutive and vary gradually between neighboring images. Therefore, a series of ideal histograms representing the consecutive images could be calculated.

Sequential Histogram Fitting Algorithm (SHFA) was designed to guide the gray value transformation from the original histograms into the desired histograms according to the fitted variance features in the form of landmarks. So, when the series of original images were subjected to the series of the desired histograms, a series of desired images were obtained, in which the brightness and contrast were adjusted. So, the processed images may better reflect the real tissue morphology than the raw captured images in visualization and future analysis.

We denoted the images in the original and the desired stacks as I_i and I'_i, where, i represents the image number in the original and desired image stacks. The histogram of I_i and I'_i were denoted by H_i and H'_i. In order to preserve the basic shape of a histogram when transforming from the original histogram H_i into the desired histogram H'_i, landmarks L_{i j} and L'_{i j} (recorded as the gray value where the landmark was set up in the histogram) were necessarily set up in the histograms H_i and H'_i, where j represents the number of landmark from left to right in each histogram.

The main procedures for obtaining the series of desired images are to be described in two steps: (1) Histogram Fitting and (2) Gray Value Transformation.

Step 1. Histogram Fitting

 The overall algorithm of the step of “Histogram Fitting” is briefly described below:

Algorithm for Step 1: Histogram Fitting

Input: Original stack of images I_i (i = 1, 2, …, N);

Output: Landmarks in original histograms L_{i j} and landmarks in desired histograms L'_{i j} (i = 1, 2, …N, j = 0,1, 2, …, M+1);

Begin:

1.  for i = 1 to N do

2.   compute the histogram H_i of I_i

3.   set up Landmarks L_{i j} (j = 0,1, 2, …, M+1)

4.  endfor

5.  for j = 0 to M+1 do

6.   compute the jth fitting curve based on L_{i j} (i = 1, 2, …, N) using fitting algorithm

7.   get the desired landmarks L'_{i j} from the computed fitting expression

8.  endfor

Firstly, all the histograms of the images in the original stack were calculated, and stored according to their image number. In order to gain both speed and accuracy, thumbnail images were processed instead of the original-sized images in this step.

Next, landmarks in each histogram were set up in order to preserve its basic shape. For landmarks L_{i j} in the original histogram H_i, the leftmost point of the whole histogram, representing the lowest gray value (usually 0), was defined as L_i0, and the rightmost point representing the highest gray value (usually 255) was defined as L_{i m+1}. The leftmost point of the dynamic range (containing useful tissue information) was defined as L_{i 1}, which was selected by searching the starting point where the gray value frequency steadily appeared. The rightmost point of the dynamic range was defined as L_{i m}, which was selected by detecting the gray value of bright background.

The landmarks L_i2, L_i3, …, L_{i m-1} were set up by dividing the span between L_i1 and L_{i m} in its corresponding cumulative histogram rather than the original histogram. Here, the cumulative histogram was transformed by integrating the original histogram, in which, the cumulative frequency T(r) were calculated as where, r represents any gray value, and p_r(r) represents the frequency of the gray value r in the original histogram. The integral of p_r(r) from 0 to r was described as T(r) (0≤r≤255, 0≤p_r(r)≤1, 0≤T(r)≤1).

The range from L_{i 1} to L_{i m} was divided evenly into m-1 spans according to the cumulative frequencies in the corresponding cumulative histogram. Then, the gray values corresponding to the landmarks of L_{i 2}, L_{i 3}, …, L_{i m-1} were determined. Finally, the basic shape of the original histogram H_i was delineated by all the landmarks {L_i0, L_i1, L_i2, …, L_{i m+1}}. The more landmarks, the more accurately the shape of the histogram was restored. Although there was a great variance of the landmark gray values in the original histogram H_i, the proportions of the spans composed of the landmarks {L_{i 0}, L_{i 1}, L_{i 2}, …, L_{i m+1}} remained almost identical between the neighboring images, since the gray values were almost the same in the adjacent bio-tissue structures. So, the neighboring landmarks should be consecutive.

Thirdly, a fitting algorithm was used on the original landmarks in order to calculate the gray values of the desired landmarks in the serial of the histograms. The landmarks were grouped according to the landmark ordinate number j, the gray values of landmarks {L_{1 j}, L_{2 j}, …, L_{n j}} could be fitted into a smoothed curve C_j. Therefore, C_j was the gray value expression describing the gray values of desired landmarks {L'_{1 j}, L'_{2 j}, …, L'_{n j}} as below:

Several complex and automatic curve fitting algorithms have been described [17,18]. When analyzing the bio-tissue images, cubic or quartic polynomial fittings[19] has proven to balance speed and accuracy of brightness compensation and contrast enhancement.

Finally, all the desired landmarks {L'_{1 j}, L'_{2 j}, …, L'_{n j}} were calculated.

Step 2. Gray Value Transformation

 The overall algorithm of the step of “Gray Value Transformation” is briefly described below:

Algorithm for Step 2: Gray Value Transformation

Input: Original stack of images I_i (i = 1, 2, …, N); landmarks in the original and desired histograms L_{i j} and L'_{i j}

Output: Desired stack of images I'_i (i = 1, 2, …, N)

Begin:

1.  for i = 1 to N do

2.   compute the desired histogram H'_i of I'_i according to H_i and the relationship between L'_{i j} and L_{i j}

3.   transform the gray values of the original image I_i according to the relationship between H'_i and H_i

4.  endfor

For the ith image, the desired landmarks {L'_{i 0}, L'_{i 1}, L'_{i 2}, …, L'_{i m+1}} and the original landmarks {L_{i 0}, L_{i 1}, L_{i 2}, …, L_{i m+1}} served as input. Now the desired histogram H'_i could be warped from the original histogram H_i. A piecewise linear transformation was used in histogram warping, i.e., the gray values [L_{i j}, L_{i j+1}] in the original histogram were converted linearly into the gray values [L'_{i j}, L'_{i j+1}] in the desired histogram. However, the spans outside of the dynamic range, i.e. [L_{i 0}, L_{i 1}] and [L_{i m}, L_{i m+1}], might be compressed after warping. So, the gray value levels were compressed, especially the gray values near L_{i 1} and L_{i m}, which might contain the useful dark or high-light information. To avoid this situation, the scale factors in the spans of [L_{i 1}, L_{i 2}] and [L_{i m-1}, L_{i m}] were adopted as the scale factors in the spans of [L_{i 0}, L_{i 1}] and [L_{i m}, L_{i m+1}] for linear transformation. The gray values below 0 or above 255 were ignored after warping. The operation above can be expressed as below:

Let piecewise scale factor be s_{i j} = (L'_{i j+1}-L'_{i j}) /(L_{i j+1}-L_{i j}); and the gray values in the original and desired histogram i be x and x': Then,

Now, any desired histogram H'_i was established. Finally, the desired image was generated by gray value transformation according to the relationship between H'_i and H_i.

Sample 1: Image Stack of E17 Kidney

The image stack of E17 kidney was used to demonstrate the performance of the proposed algorithm.

Firstly, all the image histograms were calculated, and nine landmarks (L_i1—L_i9) were selected in the dynamic range of each histogram, as plotted in solid lines, Fig 2. Next, a gray value of 64 was detected as the desired gray value of landmark L'_i1, and a gray value of 228 was detected as L'_i9. Then, a fitting algorithm was used to calculate the desired landmarks (L'_i2—L'_i8), as plotted in dashed lines, Fig 2. Afterwards, the desired histograms were calculated according to the relationship between the original and desired landmarks, Fig 3B. Finally, the gray values were transformed.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. The normalized landmarks in the dynamic range of histogram.

The solid lines represent the original landmarks and the dashed lines represent the fitted landmarks in histograms of the image stack.

https://doi.org/10.1371/journal.pone.0127855.g002

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. The comparison of result of the E17 kidney image stack before and after processing by SHFA.

(A) Histograms of the original image stack; (B) Histograms of the image stack processed by SHFA; the abscissa represents the image number, the ordinate represents gray value (0–255), and pseudo-color represents the frequencies of gray values appearing. (C) Histograms of typical images in the stack (blue for before and red for after processing), the original and processed images are shown in (D) and (E). (Image 1: good quality, Images 137 and 483: low contrast, Image 258: over-bright, Image 579: extreme low contrast). The scale bar represents 0.5 mm for all the images in D and E.

https://doi.org/10.1371/journal.pone.0127855.g003

In the original image stack, the gray values were changing dramatically and irregularly from image to image, and the dynamic ranges were located in a narrow band in the middle-to-upper part of each histogram (Fig 3A), reflecting inhomogeneous brightness and low contrast. Although the gray value distribution was changing dramatically and irregularly (Fig 3A), the proportion of two adjacent landmarks in the dynamic range was identical between the neighboring images. After processing, the histograms of the stack became regular, the dynamic ranges covered a designated area (Fig 3B), reflecting a homogeneous brightness and enhanced contrast. Representative images with different staining and contents were selected to show the results of the algorithm: Image 1 was of good quality, whereas Images 137 and 483 had low contrast, Image 258 was insufficiently stained and over-bright, while Image 579 had extremely low contrast and its tissue content was different from the other images. These original and processed images are shown in Fig 3D and 3E. Their histograms are shown in Fig 3C (blue for original images, red for processed images). The histograms of the processed images have kept all the features of the original histograms, indicating the detailed gray values have been preserved.

The result was also evaluated by visual inspection of resliced images from the three-dimensional reconstruction based on the image stack, Fig 4. The stripes in the SHFA-processed images (Fig 4B and 4D) were less pronounced than before SHFA processing (Fig 4A and 4C). These stripes results from unequal brightness of the sections, clearly disturb the histology study and data analysis. In addition, the contrast was enhanced, thus more subtle details could be recognized in the SHFA-processed resliced images.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. The resliced sections of three-dimensional reconstruction using the image stack of E17 kidney.

(A, C) Resliced images based on the original images; (B, D) Resliced images based on the images processed by SHFA, (A, B front view; C, D lateral view). The scale bar in A represents 0.5 mm, and for B, C, and D.

https://doi.org/10.1371/journal.pone.0127855.g004

Sample 2: Image Stack of P7 Kidney

The proposed algorithm was also tested with an image stack from the P7 kidney, where the tissue structures changed more dramatically in size and shape from the very first image to the middle one, and to the very last one due to the distinctive morphogenesis of an external cortex and an internal medulla. In this kidney, more tubules with thicker walls were located in the cortex than in the medulla, so that more dark stained areas were observed in cortex than in medulla. Furthermore, the convex shape of the tissue block changed from the first to the last section. In this case, SHFA proved a robust tool with a big capability for compensating uneven brightness and low contrast in a large number of serial images, Fig 5.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 5. Results of the typical images from the stack of P7 kidney processed by SHFA.

(A) Original images; (B) Processed images. The scale bar represents 1 mm for all the images.

https://doi.org/10.1371/journal.pone.0127855.g005

The stripes in the resliced images (Fig 6B and 6D) were less pronounced than before SHFA processing (Fig 6A and 6C). The stripes in the resliced images (Fig 6B and 6D) were reduced by SHFA (Fig 6A and 6C). In addition, the SHFA-processed resliced images (Fig 6B and 6D) also revealed more detailed information.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 6. The resliced sections of three-dimensional reconstruction using the image stack of P7 kidney.

(A, C) Resliced images based on the original images; (B, D) Resliced images based on the images processed by SHFA, (A, B front view; C, D lateral view). The scale bar in A represents 0.5 mm, and for B, C, and D.

https://doi.org/10.1371/journal.pone.0127855.g006